In this paper the chatter stability of turning and full-immersion milling operations with spindle speed variation is studied. We present a method to calculate the stability lobes in the limit of very low and very high frequencies of the delay modulation. These approximations help to classify the results of numerically exact methods, as for example semi-discretization or multi-frequency approaches. For slowly time-varying delay, the position of the stability lobes is understandable from a simple connection between the lobes for constant and time-varying delay. Furthermore, this method can be used to estimate the efficiency of an application of spindle speed variation and helps to find optimal parameters for it.